Autoregressive Integrated Moving Average with Exogenous Variable (ARIMAX) Model for Nigerian Non Oil Export

Abstract

This study specifically fitted an appropriate ARIMAX model for the Nigerian non-oil export using exchange rate (in dollars) as the exogenous variable by adopting the Box-Jenkins iterative three-stage modelling approach – identification, estimation and diagnostic checking. The time plot of the two series at level showed that the mean and variance are not constant but variant with time. The Augumented Dickey-Fuller (ADF) tests confirmed both series are non stationarity hence the two series were differenced once. Results of the unit roots tests in the first difference rejected the null hypotheses at 5% level of significance of non stationarity after first difference. The Autocorrelation function (ACF) and Partial autocorrelation function (PACF) combined patterns suggested AR(2) and MA(6) respectively. By comparing their various Akaike information criteria (AIC), the parsimonious model was estimated as ARIMAX (2,1,5). The goodness of fit test confirmed the adequacy of the estimated model. All the roots of the estimated ARIMAX process lie inside the unit circle. The plots of the residuals are mostly uncorrelated, the actual and the fitted agreed very closely. In addition, Q-statistics and LM test both indicate serial non-correlation. Result from the estimated model implies that exchange rate has no impact on Nigerian non-oil as exchange rate failed to be significant.

Keywords: Non-oil export, ARIMAX model, exogenous variable.